Elastothermodynamic Damping in Composite Materials

When a composite material is subjected to a stress field (homogeneous or inhomogeneous), different phases undergo different temperature fluctuations due to the well-known thermoelastic effect. As a result irreversible heat conduction occurs within each phase and between phases, and entropy is produced; this entropy is the genesis of elastothermodynamic damping. In this paper we take the second law of thermodynamics as our starting point and calculate the elastothermodynamic damping of an N-layer medium with perfect or imperfect thermal interfaces in a rectangular, cylindrical, and spherical co-ordinate system. Each layer of the composite may be subjected to any stress state so long as the resulting heat conduction can be described by a single spatial co-ordinate orthogonal to the layering. By way of illustration, results are presented for the following boundary value problem: an JV-layer periodic medium with a two-layer unit cell and a perfect or imperfect thermal interface. Two canonical mechanical states are considered: (1) a time-harmonic uniform stress perpendicular to the layering, and (2) a time-harmonic uniform strain parallel to the layering.